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I am undertaking a study where we analysing the fine details of two multiple regression equations.

Multiple regressions were carried out for the months of February and August 2017, with ET as the dependent variable and sunshine hours, relative humidity and wind speed as the independent variables.

Question:

From looking at tables 1, and 2, which (if any) of the independent variables would you consider removing from these multiple regressions and why?

Problem

Both P-values (see tables 1 and 2) are significant for both multiple regression analysis in Feb 2017 (p=5.84e-13) and March 2017 (1.93e-14). Therefore, I assume the answer is no because

All the coefficients in both models (see tables 1 and 2) are less than 0.05 so all contributions are statistically significant. From the onset, it is easy to assume there is no reason to remove any coefficients from the model.

However, some of the coefficients have a negative relationship with the dependent variable (ET), and I am confused if these influences would have deleterious consequences on the overall model.

In the likelihood that it is better to remove coefficients from the model, I would be deeply appreciative if anyone could help me to understand why?

Table 1: Feb 2017 enter image description here

Table 2: August 2017

enter image description here

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  • $\begingroup$ These tables provide insufficient information to answer the question. The question itself revolves around the correlation structure of the independent variables, whereas these tables directly reveal only information about how the dependent variable is related to the independent ones. Although this does disclose some partial information, it's not enough to answer the question. (One could offer plausible suggestions based on subject-matter knowledge, but not solely on these tables.) $\endgroup$ – whuber Mar 5 at 14:48
  • $\begingroup$ In your opinion (at the base level), having only the information provided in the tables (because we don’t have the data), would I be correct in anecdotally saying ’no’, don’t remove the coefficients. However, I could state that ideally, there is not enough information to answer this question properly if the data was available. Then I could suggest that in ideal conditions, we could test for multicollinearity between the independent variables by plotting the independent variables in scatter plots. Also, other tests of normality and variance could be used to confirm or deny model assumptions. $\endgroup$ – Alice Hobbs Mar 5 at 15:44
  • $\begingroup$ Many thanks for you feedback and advice :) $\endgroup$ – Alice Hobbs Mar 5 at 15:44

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